Ask The Author
Given the wiki page says that "submission must be submitted by the author of the work", one obvious way to do it would be to ask the original authors to take the time to submit their work. You can send them an email explaining the benefits of having their work be part of the free culture showcase. Like "exposure to millions" of users.
Dear Johnny McArtist,
I was impressed by your work, "unicorn with rainbow", and I would like to see it be part of the Ubuntu Free Culture Showcase.
"The Ubuntu Free Culture Showcase is an opportunity to show off high quality free culture content in Ubuntu. At the heart of Ubuntu's ethos is a belief in showcasing free software and free culture, and with each development cycle we open the opportunity for any artist to put their work in front of millions of Ubuntu users around the world." (via the Ubuntu wiki)
In order to submit your work, please add it to the Ubuntu Free Culture Showcase
(vimeo, flickr, soundcloud).
(some links explaining Ubuntu/Free Culture/Creative Commons, if applicable)
Thank you very much,
Assuming the licensing is in order, this should give you a good chance at getting your favourite work into the FCS.